MASS, SALT, AND HEAT TRANSPORT ACROSS
uCn LATITUDE IN THE ATLANTIC OCEAN BASED ON
IGY DATA AND DYNAMIC HEIGHT CALCULATIONS
Tommy Darell Greeson
DUDifY KNOX LIBRARY
NAVAL HJSTGRADL'ATE SCHOOL
mONTLRlY. CALIFORNIA 9<W«U
AVAL POSTGRADUATE SCHOOL
Monterey, California
THE!
MASS, SALT, AND HEAT TRANSPORT ACROSS
40°N LATITUDE IN THE ATLANTIC OCEAN BASED ON
IGY DATA AND DYNAMIC HEIGHT CALCULATIONS
by
Tommy Darell
Greeson
September
197^
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Mass, Salt, and Heat Transport Across
40°N Latitude in the Atlantic Ocean Based
on IGY Data and Dynamic Height
Calculations
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Master's Thesis;
September 197^
6. PERFORMING ORG. REPORT NUMBER
7. AUTHORf«;
Tommy Darell Greeson
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Naval Postgraduate School
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September 1974
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Heat Transport
40°N Atlantic Ocean
20. ABSTRACT (Continue on reveree elde II neceeemry mnd Identity by block number)
This study discusses the development of a computer program
capable of performing the necessary dynamic computations to
obtain estimates of the transports of mass, salt, and heat
across the vertical cross section at 40°N within the North
Atlantic Ocean. Previous studies have used either different
approaches to the problem or, if the same approach was used,
then the data were averaged to eliminate seasonal effects.
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(20. ABSTRACT Continued)
Temperature and salinity data from Crawford Cruise 16,
2 to 22 October 1957 of the International Geophysical Year,
are used for the entire cross section of ocean. These
observations provide data that are both homogeneous and
consistent .
General interpolation methods are evaluated for determining
the temperature and salinity observations at standard depths.
A combination of linear and mean parabolic interpolation methods
is found to be the most accurate method of estimating the
continuous vertical temperature and salinity, profiles at each
station.
The velocity estimates are obtained for the cross section
by the classical dynamic method. A level of no motion is
established where there is a balance of the net transports of
mass and salt.
Based on this level of no motion, a heat transport figure is
obtained that compares favorably with those of earlier studies
by Sverdrup, Jung, and Budyko.
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Mass, Salt, and Heat Transport Across
40°N Latitude in the Atlantic Ocean Based on
IGY Data and Dynamic Height Calculations
by
Tommy Darell Greeson
Lieutenant Commander, United States Navy
B.S., Clemson University, 1962
Submitted in partial fulfillment of the
requirements for the degree of
MASTER OF SCIENCE IN OCEANOGRAPHY
from the
NAVAL POSTGRADUATE SCHOOL
September 197^
7^*
DUl LirRARY
' r' - SCHOOB
ABSTRACT M0N
This study discusses the development of a computer
program capable of performing the necessary dynamic computa-
tions to obtain estimates of the transports of mass, salt,
and heat across the vertical cross section at ^0°N within
the North Atlantic Ocean. Previous studies have used either
different approaches to the problem or, if the same approach
was used, then the data were averaged to eliminate seasonal
effects.
Temperature and salinity data from Crawford Cruise 16,
2 to 22 October 1957 of the International Geophysical Year,
are used for the entire cross section of ocean. These observa-
tions provide data that are both homogeneous and consistent.
General interpolation methods are evaluated for deter-
mining the temperature and salinity observations at standard
depths. A combination of linear and mean parabolic interpola-
tion methods is found to be the most accurate method of
estimating the continuous vertical temperature and salinity
profiles at each station.
The velocity estimates are obtained for the cross section
by the classical dynamic method. A level of no motion is
established where there is a balance of the net transports of
mass and salt.
Based on this level of no motion, a heat transport figure
is obtained that compares favorably with those of earlier
studies by Sverdrup, Jung, and Budyko.
TABLE OF CONTENTS
I. INTRODUCTION 11
II. BACKGROUND 13
A. HEAT TRANSPORT . 13
B. DETERMINATION OF THE LEVEL OF NO MOTION 14
III. STATEMENT OF THE PROBLEM 20
IV. PROCEDURE 24
A. DATA SOURCES 24
B. DEVELOPMENT OF THE COMPUTER PROGRAM 29
C. SELECTION OF THE INTERPOLATION METHOD 29
D. COMPUTATIONS OF VELOCITIES AND THE
TRANSPORTS OF MASS, SALT CONTENT,
AND HEAT 30
V. DISCUSSION OF RESULTS 44
A. ' COMPARISON OF VARIOUS INTERPOLATION
METHODS 44
B. LEVEL OF NO MOTION 52
C. VELOCITIES 61
D. TRANSPORTS OF MASS, SALT, AND HEAT 70
E. WATER MASSES AND THEIR RELATIVE LOCATION
TO THE LEVEL OF NO MOTION 76
VI. CONCLUSIONS AND RECOMMENDATIONS 8l
APPENDIX A: COMPUTER PROGRAM 83
APPENDIX B: T-S DIAGRAMS FOR CRAWFORD STATIONS
218-255 93
APPENDIX C: LATITUDE AND LONGITUDE FOR CRAWFORD
STATIONS 218-255 132
BIBLIOGRAPHY I3H
INITIAL DISTRIBUTION LIST 136
LIST OP FIGURES
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Crawford' s transit of the North
Atlantic Ocean at 40°N, 2-22
October 1957
25
Vertical cross section of the North
Atlantic Ocean at 40°N showing the
vertical and horizontal extent of
temperature and salinity observations 26
Illustration of the averaging process
in order to make values of velocity,
density, temperature, and salinity
compatible within a sample rectangular
area
Illustration of the summation process
performed in the computer program for
a sample cross section of ocean
34
37
Vertical cross section through the
North Atlantic Ocean at 40°N showing
the deepest level common to a pair of
stations for which the transports of
mass, salt, and heat are computed
40
Vertical cross section through the
North Atlantic Ocean at 40°N showing
the areas for which the estimates of
the transports of mass, salt, and
heat are made from extrapolated
temperature and salinity values
Computer plot of the linear interpo-
lation method for the vertical tempera-
ture profile at Crawford Station 221 —
Computer plot of the mean linear-
parabolic interpolation method for
the vertical temperature profile at
Crawford Station 221
41
47
48
Figure 9 Computer plot of the piecewise-cubic
polynomial interpolation method for
the vertical temperature profile at
Crawford Station 221
49
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Computer plot of the combination linear
and mean parabolic interpolation method
for the vertical temperature profile at
Crawford Station 221 50
Comparison of the level of no motion
determined solely from Crawford data
with the level of no motion determined
after the inclusion of all areas in the
vertical cross section not covered with
Crawford data 57
Surface geostrophic velocities at 40°N
within the North Atlantic Ocean 63
Geostrophic velocities at 1000m within
the North Atlantic Ocean at 40°N 64
Geostrophic velocities at 2000m within
the North Atlantic Ocean at 40°N 65
Geostrophic velocities at 3000m within
the North Atlantic Ocean at 40°N 66
Geostrophic velocities at 4000m within
the North Atlantic Ocean at 40°N 67
Surface current observations "Gulf
Stream '60" (Fuglister, 1964) 68
Integrated transport of mass for
Crawford Stations 218-255 71
Integrated transport of salt for
Crawford Stations 218-255 ■ 72
Integrated transport of heat for
Crawford Stations 218-255 73
Relative position of the level of no
motion to the various water masses
within the North Atlantic Ocean at 40°N — 79
LIST OF TABLES
TABLE I Comparison of the effect of various
interpolation methods on the trans-
ports of mass, salt content, and heat
at i*0°N within the North Atlantic
Ocean 51
TABLE II Level of no motion for each pair of
Crawford Stations at 40°N within the
North Atlantic Ocean 53
TABLE III Integrated transports of mass, salt,
and heat 55
TABLE IV Transports of mass, salt, and heat
including all areas not covered by
Crawford data 58
TABLE V
TABLE VI
Comparison of the net transports of
mass, salt, and heat for the vertical
cross section at 40°N within the North
Atlantic Ocean when
level of no
motion is varied 50m above and below
the level of no motion obtained from
actual Crawford data
Comparison of heat transport values
60
75
ACKNOWLEDGMENTS
The writer wishes to thank Dr. Glenn H. Jung for his
assistance and guidance in the preparation of this thesis
and Dr. J.J. von Schwind for his constructive review of
the text .
10
I. INTRODUCTION
It has long been recognized that the earth and its
atmosphere receive a surplus of heat at the equator and lose
more heat at the poles than is received from the sun. Since
the poles of this system are not becoming progressively
colder, nor the equatorial regions progressively warmer,
there must be a transfer mechanism within the system that
transports heat from the equatorial regions to the poleward
regions of the earth. The excess heat lost at the earth's
poles is balanced by a meridional transfer of heat from
low latitudes in both the atmosphere and the oceans. How
this heat transfer is partitioned between the atmosphere
and the oceans still remains a question although a number
of studies have considered this problem in recent years
(Sverdrup, 1957; Budyko, 1956; Jung, 1955; Bryan, 1962).
Jung (1952) was one of the first to point out that the
ocean currents might be of greater significance in trans-
ferring heat energy than had been previously assumed. He
made an extensive study (1955) in an attempt to clarify
how heat is transported by deep ocean currents in the North
Atlantic Ocean. This investigation was one of the first
attempts to compute heat transport based on geostrophic
calculations from hydrographic data.
As stated by Bryan (1962) only the derivative of the
geostrophic velocity with respect to depth can be computed
11
directly from hydrographic data. To determine the velocity
itself an integration must be carried out, which in turn
presents the problem of choosing the correct constant of
integration. The selection of a level of no motion at which
the geostrophic velocity is set equal to zero is usually
identified with this constant.
The identification of this level of least water movement
in the oceans still remains a problem today. Different
scientists have devised various methods for determining this
level, none of which work in all cases. A discussion of
these various techniques is included in the next section.
The magnitudes of the transports of mass, salt, and heat
when based on geostrophic calculations are indirectly related
to the choice of the level of no motion through the conver-
sion of the derivative of geostrophic velocity to the velocity
itself. Since the object of this study is to compute the
transports of mass, salt, and heat across a particular lati-
tude section within the North Atlantic Ocean, considerable
effort has been devoted to the establishment of the criteria
for determining a satisfactory level of no motion.
12
II. BACKGROUND
A. HEAT TRANSPORT
The important mechanisms are the transport of sensible
and latent heat by the atmosphere and the transport of
sensible heat by the ocean. Scientific opinions have fluc-
tuated over the years as to whether the ocean or the atmos-
phere is the principle contributor to heat transport.
According to Neumann et al. (1966) such noted scientists
as Maury (1856) and Ferrel (1890) expressed views that the
ocean has the predominant role in transporting excess heat
from the equatorial regions to the polar regions of the
earth. Angstrom, in 1925, estimated that the ocean trans-
ported an amount of heat equal to that transported by the
atmosphere. Others, including Bjerknes et al. (1933) and
Sverdrup et al. (19^2) expressed agreement that the atmos-
phere predominated in the poleward transport of heat and
that the ocean was relatively insignificant. Sverdrup,
however, suggested that in certain areas heat transport by
ocean currents could be of importance.
Neumann et al . (1966) wrote: "The atmosphere appears
to be doing the lion's share of the heat transport. How-
ever, an appreciable part of the transport is latent heat,
and the latent heat transport increases from a value near
zero at about 20°N to I) x 101 cal/sec at 40°N. This latent
heat was taken from the oceans by the air, thus decreasing
13
the store of heat in the ocean and increasing the total
heat of the air. The ocean should be credited with carrying
this heat to points where it is available to the atmosphere
for a further transport poleward. If the latent heat at 40°N
is credited to the ocean, this, plus the sensible heat trans-
ported by the ocean, accounts for half of the total required
by radiation theory.
"The oceans are thus important in bringing about this
required balance through both the evaporation-precipitation
mechanism and the actual transport of sensible heat."
The present investigation is interested only in the
magnitude of transport of sensible heat by ocean currents
across the vertical cross section of the North Atlantic Ocean
at 40°N.
B. DETERMINATION OF THE LEVEL OP NO MOTION
The importance of determining an accurate level of no
motion for the computation of the transports of mass, salt,
and heat by the dynamic method has been stated previously.
Until the present no universal method has been devised that
works in all cases. Most of the methods developed in the
last 60 years for determining the level of no motion are
indirect approaches which try to find a characteristic that
relates to minimum motion in some water layer.
Sverdrup et al. (1942) recommended that the "zero" sur-
face in the ocean be determined by comparing water discharges
14
computed by the dynamic method from a horizontal reference
surface that is successively placed at different depths.
The no motion level is selected so that the net mass trans-
ported across an ocean section is zero. This, of course,
would require that the oceanographic stations span an entire
vertical cross section of the ocean which extends from shore
to shore. Preferably the stations should be taken within a
reasonable time interval to ensure the data are synoptic.
Jacobson (1916) advanced the idea that the oxygen mini-
mum in sea water corresponds to the layer with minimum hori-
zontal water motion. Wust (1935) and Dietrich (1936) developed
the idea and applied it in practice; it is known as Dietrich's
method. These two scientists believed that oxygen is lost
from sea water as a result of oxidation of organic matter
except in a thin surface layer. It was reasoned that if this
oxidation process takes place at all levels, due to biological
processes, then the minimum oxygen content is found where
the replenishment of oxygen by horizontal flow is at a
minimum because of weak motion.
When Dietrich applied his method to compute the water
transport in the Gulf Stream from the sea surface to the
oxygen minimum layer, his computations showed that the water
transport for the counter current below the Gulf Stream was
twice the amount transferred by the layer above the oxygen
minimum. This result is unrealistic and suggests that there
are serious difficulties with determining the level of no
motion in this manner.
15
The difficulty is underscored by Seiwell (1937) who
examined the causes for minimum oxygen concentrations at
intermediate depths in the northwestern part of the Atlantic
Ocean and found that the minimum is a result of the ratio
between oxygen supply and consumption. In his studies , he
examined a hypothetical example and showed that the oxygen
minimum does not necessarily occur at a level of minimal
horizontal motion.
Parr (1938) tried to relate the vertical current veloc-
ity distribution to the disturbance of the density field.
The method is based on the assumption of motion along iso-
pycnal surfaces in that the thickness of the layer bounded
by two isopycnal surfaces cannot remain constant in the
region of a current. In other words, the distance between
the two isopycnal surfaces varies in a direction perpendicu-
lar to the direction of the current. If the distortion of
the layer between two isopycnal surfaces is minimal, or no
distortion is evident, then there must be either minimal
water movement there or complete lack of water motion.
Fomin (1964) pointed out that an undistorted isopycnal layer
is a necessary but insufficient condition for the existence
of a layer of no motion in the sea. He states, "If there
is a layer with a strong vertical pressure gradient at inter-
mediate depth, then the Isopycnal layers will be least dis-
torted as compared with the overlying and underlying layers
in the presence of a strong gradient current in this layer."
16
In areas where there is no Intermediate vertical gradient
maximum, selection of an undistorted isopycnal layer is a
difficult if not impossible task.
Another method for determining the level of no motion
is described by Stommel (1956) in which the vertical com-
ponent of velocity, by mass conservation, must equal that
induced at the bottom of the frictional layer by the winds.
He determined formally the specific reference level at which
this matching occurs. When this method was applied to
Atlantis Stations 5203 (32° 00'N 63° 03'W) and 5210
(32° 00 'N 50° 4l'W), the depth of no meridional motion was
found to be about 1500m. As stated by Stommel, in that
location this was very nearly the depth of the high-salinity
anomaly water from the Mediterranean.
Hidaka (19^0) used the fact that there is mutual adjust-
ment between the current velocity field and the fields of
the physical-chemical properties of sea water to develop his
method for determining the layer of no motion. The method
was based on continuity considerations for the stationary
distribution of certain properties of oceanic water masses.
If a triangle of three oceanic stations is considered, at
the corners of the triangle there are three vertical and two
horizontal planes forming the boundaries of a prism extending
throughout the water column. As assumption is made that no
gain or loss occurs through the stationary surface boundary
and that the sum of volume transports through the remaining
17
four boundaries must equal zero. If an oceanic property
such as salinity Is considered, then the sum of the products
of salinity and volume transports through each boundary must
also equal zero.
Hidaka applied his method to the four triangles formed
by four oceanographic stations in ah attempt to find a
reference level for the conversion of relative into absolute
dynamic height topography. Hidaka' s simplification of the
condition of continuity, and the fact that his system of
equations cannot be solved with the existing accuracy of
measurements at sea, raised objections by other noted
oceanographers .
To the present, the most practical and probably the
most widely used method is that developed by Defant (19^1).
While examining the differences in the dynamic depths of
isobaric surfaces at a great number of pairs of neighboring
stations, Defant discovered a layer of relatively great
thickness in which these differences changed very little
along the vertical. The thickness of this layer in the
Atlantic Ocean ranges from 300 to 800m; its depth varies
rather uniformly in the horizontal direction, and the change
in differences in the dynamic depths of isobaric surfaces
only amounts to several dynamic millimeters. Defant assumes
that this water layer is almost motionless and considers it
to be the layer directly adjoining the "zero" surface.
18
In a strict sense, Defant's method may be expressed as
ADA = ADB (1)
where AD, and ADR are the increments in dynamic depths
between the isobaric surfaces p„ and p ,, at stations A
n n+1
and B. This states that the differences In the dynamic
depths of isobaric surfaces at some depth interval are
equal at two neighboring stations A and B.
As pointed out by Fomin (1964), it is doubtful whether
the layer with similar differences can be identified with
the layer of no motion when the current computed by the
dynamic method has the same direction above and below the
"zero" layer.
Jung (1955) emphasized that the level of no motion is
still an open problem although the Sverdrup approach appeared
the most reasonable solution. He recommended that the problem
be investigated further when sufficient data were available.
19
III. STATEMENT OF THE PROBLEM
This study consists of four parts: (1) the development
of a program for the IBM 360/67 computer that performs the
calculations necessary to arrive at values for mass, salt,
and heat transport across a section of the ocean; (2) the
evaluation and selection, from various interpolation schemes,
of the one which performs the interpolation to standard
depths with the best accuracy; (3) the establishment of a
reference level for which the mass and salt transports equal
zero and, based on this reference level, (4) the computation
of the transport of sensible heat by the ocean currents
across the selected vertical section.
The transfer of energy through a vertical cross section
of the ocean is accomplished by processes such as large-scale
advection, smaller-scale eddy diffusion, and molecular diffu-
sion. Large-scale advection is the principal contributor in
determining the transfer of energy while eddy and molecular
diffusion contributions are several orders of magnitude
smaller. Eddies smaller than approximately two degrees of
longitude have been neglected. Molecular diffusion has been
neglected entirely.
Jung (1952) showed that the transfer of all forms of
energy in the ocean is very accurately approximated by the
transfer of thermal energy alone. To show this he used
Starr's (1951) general equation for the advective energy
20
flux, F, across any section of fluid,
,2
F = / (P + pcyT - pgZ + p^-) Vn dA (2)
XT.
where dA represents an element of area of the cross section
which extends along a latitude circle across the ocean and
from the surface to the ocean bottom, P is pressure, T is
absolute temperature, Z is vertical distance downward from
the ocean surface, p is the density, c is the specific heat
at constant volume of ocean water, g is the acceleration of
gravity, C is the ocean current speed, and V is the poleward
component of velocity. Assuming hydrostatic equilibrium
in the vertical, the pressure term, P, nearly cancels the
potential energy term, pgZ. This cancellation would be
exact for the case of uniform density. Further, the advec-
tion of kinetic energy has been shown to be several orders
of magnitude smaller than the transport of internal energy;
thus, upon assuming reasonable values of C, the kinetic
p
energy term involving C /2 , can be neglected. With these
simplifications, (2) can be written
F = /pc TV dA (3)
A v n
where pc TV dA closely approximates internal energy (heat
transport) and determines the total energy flux across a
vertical cross section of area dA within the ocean.
21
The specific heat of sea water, c , is assumed to have
a value of unity with the introduction of an error of less
than 1% for depths less than 6000m (see Sverdrup et al.,
1942, p. 62).
Procedures outlined by Sverdrup et al. (1942, pp.
108-411 and pp. 447-448) are used to determine the velocity
estimates in this study. In using this procedure, one must
assume geostrophic balance within the ocean. Since the
cross section of the ocean under consideration is outside
the equatorial region and only large-scale motion is
considered, this assumption seems to be valid (Jung, 1955).
Dynamic heights are determined by standard procedures
and then used to compute the velocity difference between
depths 1 and 2 in a region between pairs of stations from
V - V = — (D - D ) (4)
1 2 fl/ A BJ K J
where f is the Coriolis parameter, 2^sin <f>(fi being the
angular velocity of the earth, <J> the latitude of the station),
L is the distance between stations A and B, and D. and DR
the dynamic heights (depths) at the two stations.
As stated previously, it is necessary to establish a
level of no motion when using this computational procedure.
In this study the two criteria which must be satisfied for
the determination of this depth are
22
/pV dA = 0 (5)
A n
and
fpSV dA = 0 (6)
A n
where S is the salinity. These equations assert that the
net transports of total mass and salt must equal zero when
computed across an entire latitude section of the ocean of
area A.
Having used these criteria to establish the level of
no motion, a value is obtained for the heat transported
across the vertical cross section by ocean currents.
23
IV. PROCEDURE
A. DATA SOURCES
To perform the calculations described in the preceding
sections one needs the distribution of temperature and
salinity over the vertical cross section of ocean under
investigation. The oceanographic data collected during the
International Geophysical Year provides the numerous obser-
vations of temperature and salinity required for the compu-
tation of the transports of mass, salt, and heat across the
vertical cross section within the North Atlantic Ocean at
40°N.
The oceanographic ship, Crawford, transited the North
Atlantic Ocean along 40°N from 2 to 22 October 1957, occupying
a total of 38 oceanographic stations with observations of
temperature and salinity being collected at each station.
This particular transit was designated Crawford 16, stations
218 to 255, and hereafter, will be referred to only by these
station numbers.
These 38 stations extend along 40°N from a point off the
New Jersey coast to a point off the coast of Spain (see
Figure 1). The maximum distance between any pair of stations
is 170.93 km or approximately two degrees of longitude. The
horizontal and vertical extent of the data coverage of the
cross section is shown in Figure 2. Due to the relatively
short period of time in which the data were collected, it
2k
Figure 1. Crawford' s transit of the North Atlantic Ocean
at 40°N, 2-22 October 1957. Dots indicate stations occupied.
is assumed that the data are completely representative of
the thermal and saline distribution occurring that October
along this parallel of latitude.
Even though the temperature and salinity data collected
by Crawford provides considerable coverage for this cross
section of ocean, there are areas along this parallel for
which there are no data during the time interval of the
Crawford cruise. Two of these regions is that west of sta-
tion 218 to the North American coast and that east of station
255 to the European coast. The other areas lacking data
are the regions between the deepest Crawford observations
of temperature and salinity and the ocean floor.
The largest of these areas, that from station 218 to the
New Jersey shore, has dimensions of 489 km in the horizontal
by 165m in the vertical at station 218 to Om at the New
Jersey shore .
25
tit
Crawford 16 Station Numbers
2SO
ZM
1*1
j»£ — m
Figure 2. Vertical cross section of the North Atlantic
Ocean at 40°N showing the vertical and horizontal extent
of temperature and salinity observations. Dots indicate
observations of temperature and salinity.
26
In order to determine the relative importance of the
mass, salt, and heat transports for the area west of station
218 it was necessary to arrive at reasonable estimates of
the average density, velocity, temperature, and salinity
for this area.
The average temperatures for October for this section
were taken from the "Serial Atlas of the Marine Environment."
Values of the average October temperatures were obtained at
one degree longitude increments from 4o°N, 69°W to 40°N , 74°W
at various depths ranging from 0 to 330 feet. These monthly
averages were then averaged again to obtain a single space
average value of 13.11°C.
The monthly average of the surface current velocity was
taken from the "Pilot Chart of the North Atlantic Ocean" for
October 1973- In the section from station 218 westward, the
surface current indicated on this chart is in a southerly
direction with a velocity of 25.7 cm/sec, which is assumed
to approach the geostrophic current due to the east-west
orientation of the entire vertical cross section. The geo-
strophic current at the bottom is assumed to be zero and an
average of the surface current and the bottom current is
taken to arrive at a single average value of 12.85 cm/sec.
The average value for the salinity of this section was
determined from the work of Ketchum and Keen (1955) in which
they used depth mean salinities to show a seasonal variation
in the concentration of river water on the continental shelf
27
between Cape Cod and Chesapeake Bay. In this study, their
winter depth mean salinities at 20, 30, 40, and 100 fathoms
are averaged to arrive at the value of 33.175 ppt for the
salinity of the section from station 218 to the coast of
New Jersey.
An estimated average density value of 1.02395 g/cm^
is obtained from the work by Howe (1962). This value is an
average of values as read from his graph of Section C,
Figure 4.
The average values of temperature, salinity, density,
and current velocity obtained in the preceding paragraphs
are used to compute estimates of the transport of mass,
salt content, and heat in that part of the vertical cross
section westward from Crawford station 218 to the New Jersey
shore.
The distance from station 255 to the coast of Spain is
67km and the depth of the water is less than 150m. There-
fore, it was assumed that the conditions were the same as
those between stations 254 and 255. With this assumption,
it was possible to take a percentage of the transports of
mass, salt, and heat between stations 254 and 255 based on
the area eastward of station 255 to the area between stations
254 and 255.
The procedure for obtaining the estimates of the trans-
ports of mass, salt, and heat for those areas near the ocean
floor is described in a later section.
28
B. DEVELOPMENT OF THE COMPUTER PROGRAM
An existing computer program, held by the Department of
Oceanography of the U.S. Naval Postgraduate School, Monterey,
California, which computes absolute current velocities and
volume transports between pairs of oceanographic stations was
modified so as to compute values for the transport of mass,
salt content, and heat. Additional modifications were made
to allow the program to perform the necessary summing pro-
cesses in order to obtain the integrated transports for each
pair of stations, and the net transports for the entire cross
section. Also the program's capacity for the number of
standard depths and stations was increased from 24 to 48
and 48 to 60, respectively.
A copy of the computer program is included in Appendix A.
C. SELECTION OF THE INTERPOLATION METHOD
Since the observed values of temperature and salinity
at each station must be interpolated to standard depths for
computing the velocity and the various transports in the
conventional manner, the problem of selecting an interpola-
tion scheme which comes nearest to approximating the real
ocean distribution of temperature and salinity is of major
significance.
A comparison was made of four interpolation methods.
These methods include linear, mean linear-parabolic , mean
A mean linear-parabolic interpolation method Is a
numerical average of one linear plus two parabolic
interpolations .
29
parabolic, and piecewise-cubic polynomial interpolation.
The comparison was accomplished with the aid of computer
plots of each of these methods at each of the 38 Crawford
stations. Visual comparison of the actual temperature and
salinity profiles with the interpolated values at 10m incre-
ments made it readily apparent that no one method was satis-
factory in all cases. It was determined that some combina-
tion of a linear and a higher order interpolation method
was necessary to give the desired results, especially when
there was an isothermal layer near the surface. The results
of the comparison of the four different interpolation
methods and the specific interpolation method chosen for the
rest of this study are included in Section V.A.
D. COMPUTATIONS OF VELOCITIES AND THE TRANSPORTS OF MASS,
SALT CONTENT, AND HEAT
With the assumption of geostrophic balance it is possible
to use the procedure of computing dynamic heights so as to
obtain the velocity estimates for the latitude section.
A detailed description of the flow of computations is included
in the following paragraphs to aid the reader in understanding
the computer program in Appendix A, and the exact procedures
used in obtaining the transport values.
The data from Crawford Cruise 16, stations 218 to 255,
are at various depths and have to be interpolated to standard
depths. This is accomplished by the subroutine "LGTP"
(Appendix A) which is the programmed version of the combination
30
linear and parabolic mean interpolation method. The observed
values of temperature and salinity are interpolated to the
following standard depths: 0, 50, 100, 150,200, 250, 300,
350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900,
950, 1000, 1050, 1100, 1150, 1200, 1250, 1300, 1400, 1500,
1600, 1700, 1800, 1900, 2000, 2250, 2500, 2750, 3000, 3250,
3500, 3750, 4000, 4250, 4500, 4750, 5000, 5250, and 5500m.
After obtaining the interpolated values of temperature
and salinity at the standard depths, the computer subroutine
"SGTSVA" (Appendix A) is called to compute the sigma-t,
specific volume anomaly, and specific volume for each
standard depth.
With the specific volume anomaly values calculated for
each standard depth, the next step is to compute the dynamic
heights, D. This process is accomplished in the main com-
puter program. An average specific volume anomaly between
each pair of standard depths for each station is computed
according to the following equation:
J = z (z+Az) /-n
where 6 is the mean specific volume anomaly, and 6 and
6, , . x are the specific volume anomalies at the standard
(z+Az)
depths, z and z+Az, respectively. The increments, Az, are
in standard depth increments only.
The equivalent of an integration is then accomplished
using:
31
AD = 7[z-(z+Az)] (8)
where AD is the difference in the dynamic heights (depths)
between the standard depths. A vertical summation of the
AD's is carried out for each station:
lZQ AD = D (9)
The distance L between stations in (*J) is computed with
use of the computer subroutine "DSTSTA" (Appendix A) using
the following method. The length, in meters, of one degree
of latitude and one degree of longitude for each station is
computed using the equations based on Clarke's spheroid of
1866. These lengths are functions of the latitude and
longitude of each station. The two values for one degree
of latitude are averaged as are the two values for one degree
of longitude. The difference in the latitudes and the
difference in the longitudes of the two stations are
computed. The differences in degrees in latitude and
longitude of the pair of stations are multiplied by the
average values for the length of one degree of latitude and
p
The earth is approximately an oblate spheroid (a sphere
flattened at the poles). Its dimensions and the amount of
flattening are not known exactly, but the values determined
by the English geodesist A.R. Clarke in 1866 as defined by
U.S. Coast and Geodetic Survey in i860 are used for charts
of North America.
32
longitude, respectively. This procedure gives two sides of
a right triangle and the third side, the distance L, between
the two stations, can be obtained by the use of the Pythag-
orean relation.
The use of the Pythagorean relation to obtain the third
side of a right triangle involves a flat earth assumption.
This assumption seems to be reasonable since the maximum
distance between any pair of stations is 170km.
With the distance L computed, the computer subroutine
"GEOCUR" (Appendix A) computes the relative velocity between
pairs of stations at each standard depth according to (4).
The relative velocities can be converted to absolute veloci-
ties by setting the geostrophic velocity at an assumed level
of no motion equal to zero. The computational procedure
used for determining the level of no motion from (5) and (6)
is discussed later in this section.
The velocity values obtained by the preceding method
represent values at standard depths between a pair of sta-
tions. The velocity values are averaged in the computer
subroutine "GEOCUR" to obtain a velocity in the center of
an area bounded by the two stations in the vertical and by a
pair of standard depths in the horizontal. This procedure
(denoted as Step 1) is illustrated in Figure 3.
Density is computed from the following equation:
p = —±- (10)
o±r Otomp
33
sta zn
v,
STEP 2
. g *****
T,,T,+T,
1 a
STEP 2
STA 220
STEP i
.STEP3
*«-— : i —
v „ W*
• c Z
• -*-
/! .
f -T,»Tt
STEP 3
STEP 1
50 M • fs,1».,s3
STEP^
'ts
.Tt+fr
2.
STEPfc
few.
Figure 3. Illustration of the averaging process in order
to make values of velocity, density, temperature, and
salinity compatible within a sample rectangular area.
3*J
where PSTp is density at a particular salinity, temperature,
and pressure, and agTp is the specific volume at a particular
salinity, temperature, and pressure.
Since density is computed at standard depths for each
station, one has available values for density for the four
corners of the rectangular area described in a preceding
paragraph. These four values of density are averaged to
obtain a value of average density compatible with the
average velocity for that rectangular area. The average
values of temperature and salinity are obtained in the same
manner. This procedure, illustrated in Figure 3, is accom-
plished in two steps. Step 2 is carried out in the main com-
puter program and the values are stored in a matrix array
until they are needed by the computer subroutine "GEOCUR"
where Step 3 is performed. This averaging procedure is per-
formed for each rectangular area formed by a pair of stations
and a pair of standard depths for the entire vertical cross
section. In summary then, the values are either passed to
or computed in the subroutine "GEOCUR" for each rectangle are
the area, the average density, the average velocity, the
average temperature, and the average salinity. The product
of the first three gives the mass transport, which when
multiplied In turn by each of the remaining averages gives
the heat transport and salt transport across a particular
rectangular area of the vertical cross section.
35
The transport values computed for each rectangular area
are summed both horizontally and vertically. By summing
vertically between each pair of stations, one obtains values
for the integrated transports of mass, salt, and heat for
that pair of stations. The transport values between each
pair of standard depths, for example 0 to 50m, are summed
horizontally to give the net transports of mass, salt, and
heat in a particular layer of the North Atlantic Ocean at
40°N. These layer values are then summed vertically to
give the total net transports of mass, salt, and heat across
the entire vertical cross section.
This process is accomplished by the computer program;
an example of the method is shown in Figure 4. Wherein
it is understood that the transports of mass, salt, and
heat have been computed individually for each of the rectan-
gular areas 1 thru 9. For example; the sum of the mass
transports for the rectangular areas 1, 4, and 7 gives the
integrated mass transport, A, between the pair of stations,
218 and 219. The integrated values for salt and heat trans-
port are computed for each pair of stations in the same
manner. Similarly, the mass transport values for the rectan-
gular areas 1, 2, and 3 gives the net mass transport, B,
for the layer between 0 and 50m extending from station 218
to station 221.
The computer program computes the transport values for
each pair of stations down to the deepest standard depth
36
w
-p CD
a-p
Ocean Surface
218
219 220
221
0
i
?
3
50
^
4
5
6
ion
7
8
9
150
t
A
B
Figure 4. Illustration of the summation process performed
in the computer program for a sample cross section of ocean,
A represents integrated transport for a pair of stations
218-219. B represents the net transport for the layer
0 to 50m.
common to both stations. Thus, account is not taken for
small areas, mentioned previously, of ocean near the bottom
where there are no computed values for the transports. The
areas in question are represented in Figure 5 as the areas
between the bottom of the ocean and the first solid line
above the ocean bottom. The solid line above the ocean
bottom indicates the deepest depth common to each pair of
stations for which the transports are computed. The method
for obtaining the estimates of the transports for these
37
triangles or quadrangles Is described in the following
paragraph.
Values of temperature and salinity were extrapolated
to depths deep enough to cover the entire water area between
each pair of stations. In some cases this involved an
extrapolation of temperature and salinity into the ocean
floor as If the ocean bottom did not exist. The transport
values were then computed via the computer program and a
percentage value of the water area to the total area present
in each rectangle was multiplied by the values of mass,
salt, and heat transports for each rectangle. After this
process was completed for each of the triangles or quadran-
gles, a summation was carried out to obtain the estimated
net transport values for mass, salt, and heat. The number
of areas involved is illustrated in Figure 6. It is recog-
nized that this is only a rough estimate due to the fact
that the bottom is not smooth and orderly. Once these values
are obtained they are assumed to be constant.
Each time the level of no motion is varied the integrated
transports will vary. If the integrated transports are
recorded for each level of no motion for each pair of sta-
tions, it is possible to determine the amount of change in
the integrated transports for a change in the level of no
motion. For example, the integrated transports are recorded
for the pair of stations, 235-236, with the level of no motion
set at 1000m and then at 1050m. The difference between the
38
Figure 5. Vertical cross section through the North
Atlantic Ocean at 40°N showing the deepest
level common to a pair of stations for which
the transports of mass, salt, and heat are
computed. Numbers across the top of the
figure represent Crawford stations 218 to 255
Figure 6. Vertical cross section through the North
Atlantic Ocean at 40°N showing the areas
for which the estimates of the transports
of mass, salt, and heat are made from
extrapolated temperature and salinity values.
Values of temperature and salinity are
extrapolated for every intersection of
dashed lines. Darkened areas are considered
to have negligible transports of mass, salt,
and heat .
39
no
41
transport figures is the amount of change when the level
of no motion is shifted from 1000m to 1050m.
The above procedure is used only for Crawford stations
222 to 253- The shaded areas in Figure 6 along the conti-
nental slope of both the United States and European coasts
are considered to have negligible transports of mass, salt,
and heat.
To show that the mass and salt balance obtained with the
inclusion of the mass and salt transport estimates in the
areas for which there are no actual data, causes only slight
variations in the level of no motion obtained by a mass and
salt balances based only on Crawford data, the following
procedure was adopted. First a level of no motion was
determined by balancing the mass and salt transports across
the portion of the vertical cross section covered by the
Crawford data only, i.e., all areas not covered by Crawford
data were neglected. Next a level of no motion was deter-
mined by balancing the mass and salt transports across the
vertical cross section which included those estimates of the
transports of mass and salt for the areas not covered by
Crawford data. If the level of no motion obtained by the
first approach agreed reasonably well with the level of no
motion obtained in the second approach, it was assumed that
the level of no motion obtained from Crawford data only was
the best approximation of the level of no motion for this
cross section of ocean since It was based on actual data.
42
The level of no motion was determined by balancing the
mass and salt transports across the entire vertical cross
section. This is accomplished by setting a constant level
of no motion equal to a standard depth into the computer
program, for all pairs of stations and computing the net
transports of mass, salt, and heat for the entire cross
section of the ocean. This procedure was repeated for a
different standard depth until the net transports of mass
and salt change sign. In this particular computer program
positive values indicate northward movement and negative
values southward movement. If a level of no motion speci-
fied for any particular pair of stations was deeper than the
data for the two stations, the program automatically used
the deepest level common to both stations.
Once the net transports of mass and salt have changed
sign, the level of no motion is varied (by hand) for pairs
of stations until a balance of the mass and salt transports
is achieved for the entire vertical cross section of the
North Atlantic Ocean at 40°N.
43
V. DISCUSSION OF RESULTS
A. COMPARISON OF VARIOUS INTERPOLATION METHODS
It was not until this work was completed that the work
of Borkowski and Goulet (1971) was discovered. They recom-
mend the use of linear interpolation at the top and bottom
of the profile and mean parabolic interpolation otherwise.
This recommendation came as a result of a comparison of ten
different interpolation methods with values obtained from
an in situ STD (salinity-temperature-depth) recorder.
The same conclusion was drawn by the author after making
a comparison of four different interpolation methods at each
of the 38 Crawford stations. While comparing these four
interpolation methods, it became apparent that two problem
areas existed. The first problem area is at stations that
have an isothermal layer near the surface; the second problem
area exists at all stations that exhibit a permanent thermo-
cline. As a general rule, higher order interpolation methods
overestimate the temperatures in the isothermal layer while
the linear interpolation method overestimates the temperatures
in certain areas of the permanent thermocline.
Crawford Station 221 is specifically singled out for
illustration of the comparison process due to the indications
of the isothermal layer at the surface and the steep thermo-
cline below this layer. Figures 7, 8, 9, and 10 are computer
plots of the vertical temperature profile for this station.
W
The crosses represent the observed values of temperature
while the continuous line represents values of temperature
interpolated at every 10m using the various interpolation
methods.
Figure 7 is a plot of the linear interpolation method.
This method provides satisfactory interpolated values for
the isothermal layer between the surface and the 2nd observed
values in Figure 7, but does not give as good an approxima-
tion of the temperature distribution as some of the other
interpolation methods in the area of the 3rd, 4th, and 5th
observed temperature values.
Figure 8 is a plot of the mean linear-parabolic inter-
polation method. This interpolation method is a numerical
average of the combination of two parabolic interpolations
plus one linear interpolation for a specific standard depth.
One of the three-point parabolic interpolations includes
the observed values two depths above and the observed value
one depth below the standard depth. The other three-point
parabolic interpolation includes the observed value one
depth above and the observed values two depths below the
standard depth. It is obvious from the plot that this inter-
polation method does not provide satisfactory values for
temperature in the region of the isothermal layer between
the surface and the 2nd observed temperature value.
In Figure 9, a piecewise-cubic polynomial interpolation
method is shown. This interpolation method tends to produce
45
even higher values of temperature in the isothermal layer,
plus a slight exaggeration of the profile between the 3rd,
4th, and 5th observed temperature values. Another disadvan-
tage of the piecewise-cubic polynomial interpolation is that
it requires more computer time than the other interpolation
methods .
The interpolation method finally adopted for use in this
research is a combination of linear interpolation between
the first two observed values and the last two observed
values with a mean parabolic interpolation method for the
rest of the profile. The mean parabolic interpolation was
used because the work by Borkowski and Goulet (1971) showed,
by statistical means, that the mean parabolic interpolation
method was more accurate in the nonlinear portion of the
profile. This method is illustrated in Figure 10.
A comparison of the previously discussed interpolation
methods., with the exception of the piecewise-cubic polynomial
interpolation method, is made to determine the effect of the
interpolation method on the net transports of mass, salt
content, and heat across the entire vertical cross section.
If the level of no motion is held constant then variation
in the transport values is entirely due to the different
interpolated values of temperature and salinity as obtained
by the different interpolation methods.
As can be seen from Table I, there is a considerable
difference in the magnitude of the transports computed by
46
Temperature (°C)
020
02S
E
& o
.p O
<L> *o
Figure 7. Computer plot of the linear interpolation
method for the vertical temperature profile at Crawford
Station 221. Crosses represent observed values.
Continuous line represents values interpolated every 10m,
H7
00'
Temperature (°C)
023
025
f3
K-
V.'
s-*.
JG
e
-P
o
o,o
Q)
rH
n
X
O
1^
Figure 8. Computer plot of the mean linear-parabolic
interpolation method for the vertical temperature
profile at Crawford station 221. Crosses represent the
observed values. The continuous line represents values
•interpolated every 10m.
l\S
Temperature (°C)
003
00£
OiO
OiS
020
025
o
C3
— £=>
o
f—
o
•
► -
Depth
(xlOOm)
1
1
^
<
o
o
>
(
■
Figure 9. Computer plot of the piecewise-cubic polynomial
interpolation method for the vertical temperature profile
at Crawford station 221. Crosses represent the observed
values. The continuous line represents values interpolated
every 10m.
^9
oc-c
DCS
Temperature (°C)
010 211
ozo
oze>
xi a
-P o
Figure 10. Computer plot of the combination linear and
mean parabolic interpolation method for the vertical
temperature profile at Crawford station 221. Crosses
represent the observed values. The continuous line
represents values interpolated every 10m.
50
TABLE I
Comparison of the Effect of Various Interpolation
Methods on the Transports of Mass, Salt Content,
and Heat at 40°N within the North Atlantic Ocean.
(Positive values indicate northward transport and
negative values indicate southward transport.)
Level of No Motion Held Constant
(All Values x 1012)
Interpolation
Method
Mass
gm/sec
Salt
gm/sec
Heat
gm-cal/sec
Linear
- 1.75^3 - 53.9933
- 316.9080
Mean Linear-
Parabolic
- 0.4966
8.8255
+ 48.1338
Combination
of Linear and
Parabolic Mean - 0.2677
- 0.5861
+ 114.4340
51
the linear interpolation method when compared with the other
two. One explanation for this difference can be traced to
the observations of temperature and salinity which are missing
between the depths of 200m and 1295m at Crawford Station 220.
The other 37 stations have observations of temperature and
salinity in this depth region at approximately 100m incre-
ments; therefore, the use of the linear interpolation method
would not have as drastic an effect at these stations. The
cause for the large variation is illustrated in Figure 10.
Assume that the observations of temperature and salinity
are missing between the 5th and 13th observations for station
221, and that one is using the linear interpolation method.
The line drawn in Figure 10 illustrates the resulting linear
interpolation for this region. Higher temperatures at the
standard depths would be obtained and these values, coupled
with large negative velocities, would account for the large
deviation in the transport values obtained by this method.
In this case, the mean parabolic interpolation method would
more closely approximate the actual temperature distribution
expected in this region.
B. LEVEL OF NO MOTION
The determination of the level of no motion for the entire
vertical cross section requires that net transports of mass
and salt across that section be equal to zero. The level of
no motion for each pair of stations based solely on Crawford
data is listed in Table II. This level of no motion is based
52
TABLE II
Level of No Motion for Each Pair of Crawford
Stations at 40°N Within the North Atlantic Ocean
(Values in parentheses represent changes in the level of
no motion as a result of taking into consideration all the
areas in the vertical cross section of ocean not covered
with Crawford data.)
Level of No Motion
Crawford Stations (Meters)
218-219 150
219-220 850
220-221 1150 (1100)
221-222 1200 (1250)
222-223 1200
223-224 1200
224-225 1200
225-226 1250 (1300)
226-227 1200 (1300)
227-228 1300 (1250)
228-229 1200
229-230 1200 (1300)
230-231 1200
231-232 1250
232-233 1200
233-234 1250
234-235 1250
235-236 1200
236-237 1200
237-238 1200
238-239 1250
239-240 125.0
240-241 1250
241-242 1200
242-243 1100
243-244 1200
244-245 1150
245-246 1200
• 246-247 1200
247-248 1200
248-249 1200
249-250 1200
250-251 1200 (1250)
251-252 1200
252-253 1150
253-254 1100
254-255 150
53
upon the balance of the integrated mass and salt transports
shown In Table III.
The sums of the different columns represent the net
transports of mass, salt, and heat across the entire vertical
cross section. The near balance of the mass and salt trans-
port columns represents an attempt to balance both of these
simultaneously. It should be noted that the balance of
either one is not equal to zero exactly. If one rounds each
of the integrated mass and salt transports to the nearest
12
whole number x 10 then the salt transport balance is off
12
by +1 x 10 while the mass transport balance is off by
12
-1 x 10 from an exact balance. The balance in Table III
represents a compromise between the best mass balance and
the best salt balance. If one attempts to balance only the
salt transport while ignoring the mass balance then it is
possible to make the net salt transport value in Table III
closer to zero. The opposite is true if the mass transport
is balanced without regard for the salt balance. When this
is done the variation in the level of no motion is only 50m
at three pairs of stations.
The second approach in determining the level of no
motion was to assume that the mass and salt transports of
the areas neglected in the first approach were significant.
Once the estimates for the transports of mass, salt, and
heat were obtained for these areas, the level of no motion
was varied between pairs of stations until a balance of the
54
TABLE III
Integrated Transports of Mass, Salt, and Heat
(Positive values represent northward transport,
negative values represent southward transport)
(All values x 1012)
Crawford
Mass
Stations
gm/sec
218-219
-0.048
219-220
7.839
220-221
-3.466
221-222
-0.718
222-223
2.588
223-224
0.144
224-225
1.328
225-226
-8.409
226-227
17.277
227-228
-20.877
228-229
3.160
229-230
.969
230-231
9.650
231-232
-9.637
232-233
0.215
233-234
-.539
234-235
9.188
235-236
-9.294
236-237
5.620
237-238
-6.622
238-239
1.301
239-240
6.987
240-241
-7.047
241-242
0.047
242-243
1.881
243-244
2.939
244-245
-1.114
245-246
1.232
246-247
-1.911
247-248
0.449
248-249
-2.800
249-250
0.389
250-251
-0.389
251-252
2.076
252-253
-1.454
253-254
-1.137
254-255
-0.084
Net
Transports
-0.268
Transports
Salt
Heat
gm/sec
gm-cal/sec
-1.679
-13.751
276.115
2223.725
•121.334
-967.546
-25.308
-202.166
98.986
854.604
-0.998
-63.565
46.447
367.518
•294.734
-2336.479
634.543
5177.051
•759.727
-6188.070
111.538
900.428
32.936
245.045
352.005
2859.991
•350.146
-2834.232
5.795
3.316
-13.904
-1.416
342.636
2817.137
■335.634
-2693.083
184.374
1394.852
•223.337
-1721.683
39.190
278.117
251.106
2015.054
•252.019
-2015.903
1.534
II.676
67.120
536.609
105.393
843.956
-40.968
-332.850
42.960
339.036
-70.292
-572.699
19.228
168.333
-98.216
-776.739
12.659
95.273
-14.214
-115.026
72.249
569.122
-51.382
-408.233
-40.494
-318.681
-3.014
-24.269
-0.586
+114.43
55
mass transport occurred. It turns out that the level of no
motion has to be varied at only 7 pairs out of 37 pairs of
stations, the maximum variation at any one pair of stations
being 100m. The new levels of no motion for the 7 pairs of
stations are shown in Table II in parentheses.
A comparison of the level of no motion obtained by both
approaches is shown in Figure 11. The solid line indicates
the level of no motion established with the first assumption:
that the areas west of station 218, east of station 255, and
near the ocean floor make negligible contributions to the
transport of mass, salt, and heat. The dashed line indicates
the variations to this level of no motion when making the
opposite assumption. It can be seen from either Figure 11
or Table II that the maximum variation in the level of no
motion using either assumption is 100m, which occurs at two
pairs of stations, 226-227 and 229-230. This would indicate
that the level of no motion determined solely from actual
Crawford data is a good approximation.
Table IV shows the magnitude of the estimates for the
various transports in those areas not covered by Crawford
data. The estimates in the fourth line of Table IV are the
estimates obtained from the computer program when the level
of no motion is varied to achieve a mass balance for the
entire cross section with those areas not covered by Crawford
data included. By summing each column in Table IV, one
obtains the net transports across the entire vertical cross
section of the North Atlantic Ocean.
56
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TABLE IV
Transports of Mass, Salt, and Heat
Including all Areas Not Covered by Crawford Data
(Positive values indicate northward transport and
negative values indicate southward transport.)
(All values x 1012)
Mass Salt Heat
gm/sec gm/sec gm-cal/sec
Estimates of the transport -6. 139 -213.540 -1842. 9^2
of mass, salt, and heat for
the area westward from
Crawford Station 218 to the
coast of New Jersey.
Estimates of the transport -.128 -H . 589 -32.026
of mass, salt, and heat for
the area eastward of station
255 to the coast of Spain.
Estimates of the transport +2.571 +81.734 +670.659
of mass, salt, and heat for
the bottom areas not covered
by Crawford data.
Estimates of the transport +4.003 +149.276 +1304.520
of mass, salt, and heat
based on the level of no
motion determined by the
mass transport balance
including the above
estimates .
Net Transports +.008 +12.881 +100.211
58
An attempt to balance only the mass transport was under-
taken since it was felt there was less chance of error in
the estimates of density than those of salinity. The values
of salinity in the region from Crawford station 218 to the
United States coast are highly variable due to considerable
river runoff from the Hudson and Delaware Rivers. It is
important to understand that various transports of mass,
salt, and heat obtained for those areas not covered by
Crawford data are very rough estimates and that there is no
way of checking their validity. The comparison of the two
levels of no motion in Figure 11 shows that there is very
little variation resulting from the two different approaches.
A comparison of the results in Tables III and IV shows there
is also very little resulting variation in the net heat
transport values for the vertical cross section. Since by
comparison of the two approaches, one obtains approximately
the same results, the level of no motion obtained by using
only the Crawford data is the one upon which the rest of
this work is based.
Table V shows the effect on the balance of mass and
salt transports, and the net transport of heat by varying
the level of no motion for each pair of stations 50m either
side of the presently established level of no motion. The
level of no motion is not varied between stations 218-219,
219-220, and 25^-255 because of their shallow depths; It is
assumed that the level of no motion Is located at the ocean
59
TABLE V
Comparison of the Net Transports of
Mass, Salt, and Heat for the Vertical Cross
Section at 40°N Within the North Atlantic Ocean
When the Level of No Motion is Varied
50m Above and Below the Level of No Motion
Obtained from Actual Crawford Data
(Positive values indicate northward transport,
negative values indicate southward transport.)
(All values x 1012)
50m above
Mass
Salt
Heat
gm/sec
gm/sec
gm-cal/sec
-3.288
-106. 991*
-728.523
Level of No Motion
(Based on Crawford Data) -0.268 -O.586 +114.43^
50m below +24.923 +911.009 +7509.230
60
floor for these stations. The differences in the transports
are considerable thus providing additional evidence that the
level of no motion obtained in this study lies somewhere in
between these limits.
C. VELOCITIES
Within the North Atlantic Ocean at latitude 40°N the
Gulf Stream Current System begins to meander and is generally
considered to have a west to east flow. It is also a region
where the system begins to diffuse; and the surface current
velocities are generally recognized as gradually becoming
weaker as one proceeds from west to east.
Geostrophic velocities were computed for every standard
depth that is common to a pair of stations. The geostrophic
velocities between each pair of stations at 0, 1000, 2000,
3000, and 4 000m are shown in Figures 12, 13, 14, 15, and 16
respectively.
The maximum surface geostrophic velocities occur between
stations 226-227 and 227-228: 44.18 cm/sec in the northward
direction and -48.45 cm/sec where the minus sign indicates
southward flow, respectively. This is probably related to
a meander of the Gulf Stream Current that crosses 40°N. The
water temperatures in this region are higher than the
surrounding water temperatures which is a further indication
that these velocities can be associated with the Gulf Stream.
Fuglister (1964) showed the path of the Gulf Stream in
the vicinity of 40°M to be complex (see Figure 17). The
61
Figure 12 Surface Geostrophic Velocities
Figure 13 Geostrophic Velocities at 1000m
Figure 14 Geostrophic Velocities at 2000m
Figure 15 Geostrophic Velocities at 3000m
Figure 16 Geostrophic Velocities at 4000m
(In the figures listed above, the vertical axis is
in cm/sec. The horizontal axis represents Crawford stations
218 to 255. Positive velocity values represent a northward
flowing current while negative values represent southward
flow. The solid arrows represent velocities computed from
the level of no motion based only on Crawford data.)
62
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SURFACE CURRENT OBSERVATIONS, GULF STREAM '60
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[From Fuglister (1964)]
68
current measurements in his study were obtained with the
use of a GEK during 2 April to 15 June i960. A comparison
of Figures 12 and 17 indicates some similarities in the
north-south pattern of the Gulf Stream even though his
measurements were taken in a different season and year than
those of this study. His i960 study was chosen for comparison
because it happens to be nearer to the time that the IGY
data were collected.
One major difference between his current pattern and
the one obtained in this study is the presence of the large
meander shown in his pattern between 6o°W and 6.3°W. The
path of the Gulf Stream plotted from various cruises conducted
in 19^7, 19^8, 1950, and i960 shows a quasi-stationary pattern
with an abrupt change near 62°W. Some years this meander
crosses 40°N and in others, it does not. According to
Fuglister, this sudden change in the pattern of meanders is
a permanent feature of the Gulf Stream.
The geostrophic velocities below the level of no motion
as determined in this study are shown in Figures lk , 15, and
16. The maximum geostrophic velocity of about +7 cm/sec
below the level of no motion occurs at a depth of ^000m
between stations 236 and 237. In most cases, for this
vertical cross section of the North Atlantic Ocean, the deep
ocean velocities are less than 3 cm/sec for the areas below
the level of no motion. In general, the stronger geostrophic
velocities at depth can be associated with the stronger
velocities at the surface.
69
The weak geostrophic velocities below the level of no
motion could be another indication that the level for this
cross section of ocean has been chosen properly.
D. TRANSPORTS OF MASS, SALT, AND HEAT
The integrated transports of mass, salt, and heat for
each pair of stations are shown in Figures 18, 19, and 20,
respectively. These figures closely resemble the geostrophic
velocity figures since the transports are directly related to
the velocity. One item to note in Figures 18 and 19 is that
the transports of mass and salt for one pair of stations
tends to be balanced by another pair of stations in close
proximity. For example, in Figure 18, the integrated north-
ward mass transport value for stations 226 to 227 tends to
be balanced by the integrated southern mass transport value
for stations 227 to 228.
This is in conformity with the assertion of Sverdrup
et al . (19^2): "If the section is taken across an ocean,
the mass transport to the north must equal the mass transport
to the south but the heat transport may differ because the
temperature of the water transported in one direction may be
higher or lower than that of the water which is transported
in the opposite direction."
Two methods are available for measuring the meridional
heat transport in the oceans. Heat balance computations are
used in one method. The addition of geothermal heat through
the ocean floor is relatively small, and the heat transport
70
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73
can be computed from the distribution of heat sources and
sinks at the surface. The second method consists of direct
computation based on measurements of velocity and temperature.
Sverdrup's heat transport estimates were obtained by
utilization of the first method. Budyko constructed maps
of the heat balance for the entire earth's surface from
which he obtained his estimates. Jung (1955) utilized the
second approach based on data from the Meteor expedition
and The Naval Hydrographic Office. Bryan (1962) used a
completely independent method based on geostrophic calcula-
tions from hydrographic data, measuring the integral of
covariance of the meridional velocity and temperature of an
entire vertical section across an ocean basin. This method
included the division of the heat transport into two parts.
One part is calculated from hydrographic data alone and is
independent of the level of no motion. The other part of
the integral does contain information about the level of no
motion, and is calculated from the field of surface wind
stress .
A comparison of the heat transport values determined in
this study is made in Table VI with the values obtained by
Jung, Budyko, Sverdrup and Byran. Of note is the discrepancy
between the author's value and that determined by Bryan. Both
studies for this cross section are based on the same IGY
data, but the methods are different. The only explanation
for the discrepancy Is that Bryan's method is limited by the
existing knowledge of the distribution of the wind stress.
7*»
TABLE VI
Comparison of Heat Transport Values
(Positive values indicate northward transport.)
TO
(All values x 10 gm-cal/sec)
Sverdrup Bryan
(1957) (1962)
40°N 40°N
+11.4 +13.5 +9.5 +18.0 +14.5* +0.0
Greeson
Jung
(1955)
Budyko
(1956)
i»0°N
36°N 45°N
40°N
interpolated value.
75
The methods of Sverdrup and Budyko eliminated seasonal
effects by using annual heat balance computations while Jung
eliminated them by averaging all data for the cross section.
Since the data used in the present study were collected
during one month, it should reflect a seasonal variation if
one exists; therefore, there is no reason why the values of
Sverdrup, Budyko, and Jung should compare favorably.
However, due to the favorable comparison of author's
heat transport value with those obtained by Sverdrup, Budyko,
and Jung, it might be suggested that the meridional transport
of heat for this cross section of ocean is quasi-stationary.
E. WATER MASSES AND THEIR RELATIVE LOCATION
TO THE LEVEL OF NO MOTION
Figure 21 is a representation of the distribution of the
water masses present at 40°N within the North Atlantic Ocean
The basis for this figure are the T-S diagrams of Crawford
stations 218-255 included as Appendix B. The horizontal
discontinuous line through Regions III and IV represents
the level of no motion as determined by the balance of mass
and salt transports through the vertical cross section.
Sverdrup et al. (19*12) defined the North Atlantic Central
Water (Region II) as water that is characterized by a nearly
straight T-S curve between the points T=8°C, S=35.10 ppt ,
and T=19°C, S=36.70 ppt, and North Atlantic Deep and Bottom
Water (Region V) as characterized by temperatures between
3.5°C and 2.2°C, and salinities between 3^-97 and 3^-90 ppt.
76
According to Sverdrup, between these two typical water masses
are found other water masses, most of which have not been
formed in the North Atlantic Ocean but which exercise a
considerable influence upon the distribution of temperature
and salinity at mid-depths. .
The regions depicted as II and V in Figure 21 represent
the area for which values of temperature and salinity fall
within the limits defined by Sverdrup for the North Atlantic
Central Water and the Deep and Bottom Water.
Region I represents the surface area that experiences
highly variable temperatures and salinities due to evapora-
tion and precipitation. Regions III and IV represent areas
where the temperatures and salinities fall outside the limits
that define the North Atlantic Central, and Deep and Bottom
water masses. The reason for dividing this intermediate
water region into two areas is that a good portion of it is
affected by the high temperature and high salinity water of
the Mediterranean Sea, Region III representing the Mediter-
ranean influence. The limits of the region were determined
from the T-S diagrams in Appendix B. While it Is understood
that the limits of the region can not be defined precisely
by this method, it does give a good relative picture of the
influence of the Mediterranean water at this particular
latitudinal cross section. The asterisks indicate the
salinity maximum determined from the T-S diagrams.
77
Figure 21. Relative position of the level of no motion
to the various water masses within the North Atlantic Ocean
at iJ0°N.
I. Surface Water
II. North Atlantic Central Water
III. Intermediate Water with Mediterranean
Influence
IV. Intermediate Water with no Mediterranean
Influence
V. Deep and Bottom Water.
78
79
Region IV is the intermediate water area that falls
outside the limits of the North Atlantic Central, and Deep
and Bottom water masses, and shows no influence of the
Mediterranean water. There is a slight indication of the
presence of Arctic Intermediate Water in the T-S diagrams
for Crawford stations 236, 231, 227, 222, and 220; but this
is not indicated in Figure 21. Regions III and IV could
probably be more appropriately described as the areas where
more than two water masses are mixed and are represented on
a T-S diagram as the nonlinear portion that lies between the
North Atlantic Central and the Deep and Bottom water masses
of the North Atlantic Ocean.
As can be seen from Figure 21, the level of no motion
lies in the intermediate water regions. III and IV. These
regions probably represent areas of considerable vertical
mixing vice lateral mixing since the level of no motion
established in these areas requires no horizontal water
movement. Weak horizontal velocities would be prevalent in
the close proximity of this level. The author knows no
reason why the level of no motion should fall in this region
except that this is where the balance of the transports of
mass and salt occurs.
80
VI. CONCLUSIONS AND RECOMMENDATIONS
This study represents the first attempt to determine
mass, salt, and heat transports based strictly upon the
dynamic method from data which are completely homogeneous
and consistent. The results indicate that the transport
of heat is quasi-stationary; but this requires additional
investigation based upon data taken during different seasons.
Agreement between the heat transport of this study and those
of other authors is surprisingly good even though the methods
and the data were completely different.
A level of no motion has been determined that gives a
reasonable geostrophic velocity picture for the entire cross
section. It was further established that this level is net
necessarily related to any characteristic of the water nor
to a specific water mass and is shown to lie in a region
where the water masses appear to have been thoroughly mixed.
The volume of calculations for this type of study can be
accommodated easily with the aid of high speed computers.
Through the use of the computer program in Appendix A, the
remainder of the IGY data at other latitudinal cross
sections of the North Atlantic Ocean can be used to piece
together a complete picture of the heat transport. Not only
can the heat transport picture be established in the North
Atlantic, but in other oceans as well. Furthermore, the
81
velocity picture and the level of no motion can be established
where there are latitudinal cross sections with data such as
the data collected during the IGY.
82
APPENDIX A
COMPUTER PROGRAM
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92
APPENDIX B
T-S DIAGRAMS FOR CRAWFORD STATIONS 218-255
93
33.3
28
34.1
34.7
35.3
35.9
36.5
24
20
16
X
12
X" w<
X x
.vford station 218
91
33.5
28
34.1
T-
34.7 35.3
1 1 —
35.9
36.5
24
20
16
X
X
12
X
X
X
Crawford station 219
95
33.5
28
34.1
3^4.7
35.3
35.9
3a.s
24
20
16
12
4 -
fc
X
T
Irswford st /fcio r
96
33.5
38
34.1 34.7 35.3 35.9 36.5
1 1 1 i
24
20
16
X
X
X
X
12
X
X
X
X
X
X
Srcwforcl : tation 221
97
33
28
24
•5 34.1
y*.7
1
i
20
16
12
35.3
35.9
T~
;X
x
X
X
X
36.5
Cra\ ford station 22"
98
33.5
26
34.1
— r~
3M.7
i —
35.3
35.9
34.5
24
X
20
16
12
X
X
8 -
0
X
X
X
X
':-■>• —-Fn^
■:-:for- v tion 223
99
33.5
26
34J
1-
34.7
35.3
35.9
36.5
24
20
16 .
12
X
X
X
X
X
X
X
fford tatiofi ?~A
■ f-
100
33.5
28
34.1
34.7
1 —
35.3
7*
20
16
12
8 -
35.9
I
X<
X
X
X
X
X
X
X
X
36.5
Jrawford Gtation
101
33J
26
34.1
y*.7
35-3
35.9
36.5
24 -
20
16
12
6 -
< -
1
1 1
1
-
-
X
X
-
•
X
-
)
- -
X
X
X
X
-
X
X
X
v
1
yt
:>:v: ' ,_ s 'i; r. '': j. en 2 ?! 6
102
33.5
28
34.1
34.7
35.3
35.9
36.5
I
24
20
16
12
x X
X
X
X
X
X
C r v \vf o r d st a t i r >:i 227
103
33.5
28 r-
34.1
— T-
34.7
35.3
35.9
36.5
24
20
X
16
X
X
frav/ford station "22!
X
104
33.5
28
34.1
34.7
35.3
35.9
36.5
24
20
16
12
X
X
X
X
X
X
»
.-..-. -for3 station 229
105
33.3
28
24
20
16
12
34.1
34.7
1 —
2±2 359 36-3
i r
X
X
X
X
!r:.v;ford station 230
106
33.5
28
34.1
34.7
35.3
35.9
— r~
36.5
24
20
16
12
X
rt^tr...rPr.^,A _j.0j.^ nri* p "5-1
X
X
X
107
33.5
28
34.1
34.7
33.3 35.9
36.5
24
20
16
12
< -
1 ■■ 1
1
I
• • '
•
-
X
X
•
-
X
X
-
X
X
X
X
XX
X
£> .
•
'ord station "32
108
33.5
28
34.1
3*4.7 35.3 35.9
i 1 r—
34.5
24
20
16
12
X
xx
Crawford station 233
109
33.5
28
34.1
34.7
1 —
35.3
J—
35.9
36.5
24
20
16
12
X
X
X
X
X
X
X
X
2k
»■
Irawford station "234
110
33.5
38
34.1
34.7
35.3
35.9
36.5
1
24
30
16
13
X
X*
&
Crav:ford station 235
111.
33.5
28
34.1
34.7
35.3
35.9 36.5
24
20
xx
16
12
X
X
X
/
X
X
X
X
X
X
Iraw '•,"■' si bion 236
112
33.3
38
3.4.1
y4.7
35.3
35.9 34.5
24
20
16
12
X
Z
X
Crawford station 237
113
33.3
28
34.1
34.7
1 —
35.3
35.9
36.5
24
20
X
X
16
X
12
X
X
X
X
X
X
X
X
X
•hi nn P ■
111
33.3
28
34.1
T-
34.7
35.3
35.9
1 —
34.5
24
20
X
X
16
12
X
X
X
Crawford station 23S
115
33.5
38
34.1
34.7
35.3
35.9
36.5
34
20 -
16
12
1
r i
1
-
1
.—
•
X
-
-
X
*
X
X
X
-
X
X
X
•
X
X
%
X
Crawford c tat ion "240
116
33.3
28
34.
34.7
35.3
1 —
35.9
36.5
24
20
X
X
16
12
X
X
X
#
X
X
X
X
n ■*».-...,•?
or stction
■h-inn p/11
117
33.5
28
34.1
34.7 35.3
1 1 —
35.9
1 —
36.5
24
20
16
12
X
X
^
X
X
X
X
X
X
X
Crawford station
118
33.3
28
34.1
r-
34.7
35.3
1 —
35.9
36.5
24
20
X
X
16
12
X
X
X
X
X
X
X
X
tf
Crawford station 243
119
33.5
28
34.1
34.7
35.3
35.9
34.5
24
20 -
16
12
1 1 1
»
1
X
.
X
1
■
X
X
X
•
■
X*
X
X
f
X
X
.
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X
X
' f
•
Crawford station 244
120
33.3
28
34.1
3-4.7
1 —
35.3
1 —
35.9
36.5
24
20
16
X
12
X
X
X
X
X
X
X
.-X
Crav/ford station 245
121
33.5
28
34.1
34.7
35.3
35.9
3d. 5
24
20
*x
16
12
X
#
X
X
X
X
X
X
X
X
M
C r c.v;i o r d s t at i o n 2 • ' 6
122
33.5
28
34.1
34.7
1 —
35.3
1 —
35.9
1 —
36.5
24
20
16
12
8 -
X
>F
X
X
s
X
X
X
X
Jrav-ford station 247
123
~3>
33.5
28
■^*L
34.1
34.7
24
-..:"■.
•• ' >,"
20
16
12
35.3
35.9
r-
X
X
X
X
*x
X
X
X
#
#
36.5
Crawford station 24°
124
33.3
28
34.1
— T"
34.7
— r —
35.3
1 —
35.9
36.5
24
20
XX
16
X
12
X
X
XX .
X
X
X
.X
3$
bat ion 249
125
33.3
28
S
34.1
34.7
33.3
1 —
35.9
36.5
24
20
X
16
12
X
X
X
X
X
X
Crawford station 250
126
33.5
28
34.1
r~
14.7
35.3 35.9
34.5
24
20
16
X
12
x *
X
X
X
Crawford station 251
127
33.5
28
3<.l
3*1.7
35.3
35.9
1 —
36.5
24
20
16
X
X
X
x x
*x
X
X
X
Crawford station 25
ICC
128
33.5
28
34-1
34.7
1 —
33.3
35.9
34.5
24
20
16
12
X
X
X*
xxxx
X
X
X
Crawford station 253
129
33.3
28
34.1
*4.7
35.3
35.9
36.5
24
20
16 -
12
A -
1 i
1
•
<
-
X
m
X
■
•
X
X
■
X
>xx
>
-
X
X
X
X
"
Crawford station 2 [ • '
130
33.5
28
34.1
34.7
— r-
35.3
35.9
36.5
24
20
16
12
Crawford station" 255
X
#
131
APPENDIX C
LATITUDE AND LONGITUDE FOR CRAWFORD STATIONS 218-255
Crawford Station
Number
Date
Oct 57
Latitude
40° 15'N
Loni
68°
gltude
218
2
25'W
219
2
Oct
57
40°
15'N
67°
58'W
220
7
Oct
57
40°
15'N
67°
20 'W
221
7
Oct
57
40°
15'N
66°
28'W
222
8
Oct
57
40°
14'N
64°
40'W
223
8
Oct
57
40°
16'N
62°
56'W
224
8
Oct
57
40°
10'N
61°
07'W
225
9
Oct
57
40°
16'N
59°
35'W
226
9
Oct
57
40°
12'N
57°
39'W
227
10
Oct
57
40°
16'N
55°
59'W
228
10
Oct
57
40°
15'N
54°
12'W
229
11
Oct
57
40°
10'N
52°
18'W
230
11
Oct
57
40°
12'N
50°
42'W
231
12
Oct
57
40°
15'N
49°
OO'W
232
12
Oct
57
40°
14'N
47°
12'W
233
13
Oct
57
40°
03'N
45°
39'W
234
13
Oct
57
40°
17'N
43°
40'W
235
14
Oct
57
40°
15'N
41°
56'W
236
14
Oct
57
40°
12'N
40°
18*W
237
15
Oct
57
40°
12'N
38°
34'W
238
15
Oct
57
40°
14'N
36°
44'W
239
16
Oct
57
40°
14'N
34°
58'W
240
16
Oct
57
40°
15'N
330
13'W
241
16
Oct
57
40°
15'N
31°
29'W
242
17
Oct
57
40°
14' N
29°
4 8'W
243
17
Oct
57
40°
14'N
27°
58'W
244
18
Oct
57
40°
14'N
26°
13*W
245
18
Oct
57
40°
03'N
24°
27'W
132
Crawford Station
Number
Date
Latitude
Longitude
246
18
Oct 57
40°
l4'N
22° 4l'W
247
19
Oct 57
40°
16'N
21° OO'W
248
19
Oct 57
40°
14'N
19° 12'W
249
20
Oct 57
40°
l8'N
17° 26'W
250
20
Oct 57
40°
15'N
15° 46'W
251
21
Oct 57
40°
13'N
14° OO'W
252
21
Oct 57
40°
14'N
12° 09'W
253
22
Oct 57
40°
15'N
10° 50'W
254
22
Oct 57
40°
16'N
09° 53'W
255
22
Oct 57
40°
14'N
09° 33'W
133
BIBLIOGRAPHY
1. BJerknes, V.F.K., J. Bjerknes, H.S. Solberg and
T. Bergeron, Physicalische Hydrodynamik. Julius
Springer, Berlin. 797 pp., 1933-
2. Borkowski, M.R. and Goulet , J.R., Comparison of methods
for interpolating oceanographic data, Deep-Sea Research,
18, pp. 269-274, 1971.
3. Bryan, K. , Measurements of Meridional Heat Transport
by Ocean Currents, J. Geophys. Res., 67 (9),
PP. 3403-3414, 1962.
4. Budyko, M.I., The Heat Balance of the Earth's Surface,
translated by N.A. Stapanova, 1958, U.S. Department of
Commerce, Washington, D.C., 259 pp., 1956.
5. Defant, A., 1941, Die absolute Topographic des
physisikalischen Meeresniveaus und der Druckflachen,
sowie die Wasserbewegungen im Atlantischen Ozean.
Wiss. Ergebn. D. Deutschen Atlantischen Exped. auf d.
Forschungs- u. Vermessungsschiff 'Meteor' — 1925-27,
VI (2 Tell., 5 Leif.), Walter De Gruyter and Co.,
Berlin and Leipzig, pp. 191-260.
6. Dietrich, G. , Aufbau and Bewegung von Golfstrom und
Agulhasstrom. Naturwissenschaften no. 15. , 1936.
7. Fomin, L.M., The Dynamic Method in Oceanography.
Chap. IV, Methods for Computing the "Zero" Surface in
the Sea, Elsevier Publishing Co., New York, pp. 117-148,
1964.
8. Fuglister, F.C., Gulf Stream '60, Ref. No. 64-4, Woods
Hole Oceanographic Institution, Woods Hole, Mass.,
pp. 265-383, 1964.
9. Hidaka, K. , Depth of motionless layer as inferred from
the distribution of salinity in the ocean. Trans. Am.
Geophys. Union, V. 30, No. 3., 1940
10. Howe , M.R., Some direct measurements of the non-tidal
drift on the continental shelf between Cape Cod and
Cape Hatteras, Deep-Sea Research, 9, 445-453, 1962.
11. Jacobsen, J. P., Contribution to the hydrography of the
Atlantic. Medd. Komm. Havundersgelser , Ser.
Hydrografi, V. 2. , 1916.
134
12. Jung, G.H. , Note on meridional transport of energy
by the oceans. J. Marine Res., 11_ (2), pp. 139-146,
1952.
13. Jung, G.H. , Heat transport in the Atlantic Ocean,
Ref. 53-34T, Dept. of Oceanography, A. and M. College
of Texas, College Station, 1955.
14. Ketcham, B.H. , and Keen, D.J., The accumulation of
river water over the continental shelf between Cape
Cod and Chesapeake Bay, Deep-Sea Research, Suppl. to
vol. 3, PP. 3^6-357.
15. Metcalf, W.G., 1958: Oceanographic Data from Crawford
Cruise 16, 1 Oct. - 11 Dec. 1957 for the International
Geophysical Year of 1957-58, Ref. No. 58-31, Woods
Hole Oceanographic Institution, Woods Hole, Mass.,
pp. 23-41, 1958. (unpublished manuscript)
16. Neumann, G. and Pierson, Jr., W. J. , Principles of
Physical Oceanography, pp. 244-247, Prentice-Hall,
1966.
17. Parr, A. 1938. Analysis of current profiles by a study
of pycnomeric distortion and identifying properties.
J. Marine. , 4.
18. Seiwell, H.R., The minimum oxygen concentration in the
western basin of the North Atlantic. Papers Phys.
Oceanogr. Meteorol., v. 3, 1937.
19. Starr, V.P., Applications of energy principles to the
general circulation. Compendium Meteor. , Amer.
meteor. Soc, Boston, ppT 568-574 , 1951.
20. Stommel, H. , On the determination of the depth of no
meriodional motion. Deep-Sea Research, 3, PP • 273-2783
1956.
21. Sverdrup, H.V. , M.W. Johnson and R.H. Fleming, The
Oceans. Prentice-Hall, New York, 1087 PP., 1942.
22. Sverdrup, H.V. , Oceanography, Handbuch der Physik.
Springer Verlag, Berlin, 1957.
23. Walford, L.A., and Wicklund, R.I., Monthly Sea
Temperature Structure from the Florida Keys to Cape
Cod, Serial Atlas of the Marine Environment, U.S.
Dept. of Sport Fisheries and Wildlife, 1968.
24. Wiist, G. , Schichtung und Zirkulation des Atlantischen
Ozeans. Die Stratosphare . WIss Ergeb . Deut. Atlant.
Exped. "Meteor", V. 6, Part 2., 1925-1927, 1935.
135
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137
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Mass, salt
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Mass, salt, and heat
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culations.
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Mass, salt, and heat transport across 40
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